We describe the kernel-based statistical distance known as Maximum Mean Discrepancy (MMD) [1]}, which has recently had a major impact in the ML community. Broadly speaking, kernel methods allow nonlinear problems involving higher-order statistics to be treated using linear methods, by embedding the set of probability distributions into a reproducing kernel Hilbert space (RKHS) [2]}, [3]}. We do not discuss the RKHS formalism, although many results are most naturally viewed in this context.
The use of MMD as a statistical distance leads naturally to a measure of statistical dependence or correlation, known here as the Hilbert Schmidt Correlation (HSCor) [4]}. These two diagnostics can provide powerful quantitative tools to study the beam dynamics processes mentioned above.
